Daily Assignments
Final Exam on Monday, December 19, 12:40 - 2:40 PM
- As scheduled by the registrar
- Practice Final one-sheet
- Practice Final with answer blanks
- Practice Final Solutions
- Solutions to Mastery Quiz 13
December 12: The Divergence Theorem and Vector Calculus
- Mastery Quiz 13 due
- M5, M6
- No answer blanks
- Answer blanks
- Read section 8.2-3 of the online notes
- Or read (sub)sections 6.8 of Gilbert and Strang
- Bonus Section 8.4 of the online notes discusses an advanced perspective on vector calculus. We will not be substantially covering it in this course, and we certainly won’t be testing on it, but you might find it interesting or enlightening.
December 9: Recitation 14 on Stokes’s Theorem and Divergence
December 7: Divergence
- Read the solutions to Mastery Quiz 12
- Read section 8.1 of the online notes
- Or read (sub)sections 6.5.1 of Gilbert and Strang
December 5: Stokes’s Theorem
- Mastery Quiz 12 due
- M5, M6, S5
- No answer blanks
- Answer blanks
- Read section 7.4 of the online notes
- Or read (sub)sections 6.7 of Gilbert and Strang
December 2: Recitation 13 on Surface Integrals
November 30: Flux Integrals
- Read the solutions to Mastery Quiz 11.
- Read section 7.3 of the online notes
- Or read (sub)sections 6.6.4-6.6.6 of Gilbert and Strang
November 28: Surfaces and Scalar Surface Integrals
- Mastery Quiz 11 due
- M4, M5, S5
- No answer blanks
- Answer blanks
- Read the Solutions to mastery quiz 10
- Read sections 7.1-2 of the online notes
- Or read (sub)sections 6.6.1-6.6.3 of Gilbert and Strang
November 21: Curl and Green’s Theorem
- Mastery Quiz 10 due
- M4, M5, S4
- No answer blanks
- Answer blanks
- Read sections 6.5-6 of the online notes
November 18: Recitation 12 on Conservative Vector Fields
November 16: Conservative Vector Fields
- The class recording is posted under “Zoom Meetings” on Blackboard
- Read section 6.4 of the online notes
- Or read section 6.3 of Gilbert and Strang
November 14: Midterm 2
- Take the practice midterm
- Read solutions to mastery quiz 9
November 11: Recitation 11 on Line Integrals
November 9: Vector Fields and Line Integrals
- Read sections 6.2-3 of the online notes
November 7: Probability and Scalar Line Integrals
- Mastery Quiz 9 due
- M4, S4
- No answer blanks
- Answer blanks
- Read section 6.1 of the online notes
- Or read section 6.2.1 of Gilbert and Strang
November 4: Recitation 10 on change of coordinates and center of mass
November 2: Integral Applications
- Read the solutions to quiz 8
- Read section 5.6 of the online notes
- Or read section 5.6 of Gilbert and Strang
October 31: Spherical Integrals and Alternate Coordinate Systems
- Mastery Quiz 8 due
- M3, M4
- No answer blanks
- Answer blanks
- Read the rest of section 5.5 of the online notes
- Or read section 5.7 of Gilbert and Strang
October 28: Recitation 9 on Polar and Cylindrical Integrals
- Apparently we didn’t get the right worksheet out, but here is the one I intended to use
- Recitation 9 Worksheet
October 26: Polar, Cylindrical, and Spherical Coordinates
- Mastery Quiz 7 due
- M2, M3
- No answer blanks
- Answer blanks
- Read the rest of sections 5.3-4 of the online notes
Recitation 8 on Iterated Integrals
October 19: Double Integrals 2
- Read the rest of section 5.2 of the online notes
October 17: Double Integrals
- Mastery Quiz 6 due
- M2, M3
- No answer blanks
- Answer blanks
- Read sections 5.1-2 of the online notes
- Or read sections 5.1
Recitation 7 on Optimization
October 12: Lagrange Multipliers and Riemann Sums
- Read the Midterm 1 Solutions
- Read section 5.1 of the online notes
- Or read section 5.1 of Gilbert and Strang
October 10: Constrained Optimization
- Mastery Quiz 5 due
- Read sections 4.2-3 of the online notes
- Or read section 4.8 of Gilbert and Strang
October 7: Recitation 6 on optimization
October 5: Optimization
- Read sections 4.1-2 of the online notes
- Or read section 4.7 of Gilbert and Strang
October 3: Midterm 1
- You may bring a one-sided, handwritten cheat sheet on letter-size or A4-size paper.
- You may bring a non-graphing calculator, but it won’t help you.
- Practice Midterm 1
September 30: Recitation 5 on the Gradient and Second Partials
September 28: The Chain Rule and Second Partials
- Read the Solutions to Mastery Quiz 4
- Read sections 3.6-7 of the online notes
- Or read section 4.6 of Gilbert and Strang, and look back at 4.3
September 26: The Gradient and the Chain Rule
- Mastery Quiz 4 due
- M1, M2, S2, S3: due
- No answer blanks
- Answer blanks
- Read sections 3.5-6 of the online notes
- Or read sections 4.5 and 4.6 of Gilbert and Strang
September 23: Recitation on Multivariable Limits and Derivatives
September 21: Linear Approximation and the Gradient
- Read the solutions to mastery quiz 3
- Read sections 3.4-5 of the online notes
- Or read section 4.4 of Gilbert and Strang
September 19: Limits and Continuity of Multivariable Functions
- Mastery Quiz 3 due
- M1, S1, S2
- No answer blanks
- Answer blanks
- Read Sections 3.2-3 of the online notes
September 16: Recitation on Graphing 3D functions
September 14: Calculus of Vector Functions
- Read the Solutions to mastery quiz 2
- Read section 2.1 of the online notes
- Some videos:
September 12: Vector Functions
- Mastery Quiz 2: Due September 12
- M1, S1
- No answer blanks
- Answer blanks
- Everyone should submit both questions on this quiz. I screwed up, and the “vectors” topic that we started last week is in fact a major topic. You get four cracks at it, and will be graded on your best two. Everything is being updated to reflect that.
- Read section 2.1 of the online notes
- Or read section 3.1 of Gilbert and Strang
September 9: Recitation 2 on Cross Products
September 7: Cross Products and Planes
- Read sections 1.4 and 1.5 of the online notes
September 2: Recitation on Projections
August 31: The Dot Product
- Read section 1.3 of the online notes
- Or read section 2.3 of Gilbert and Strang
August 29: Syllabus and Vectors
- Please read the syllabus
- Claim your account on WeBWorK through Blackboard
- Read Professor Bonin’s advice on study skills
- Read Section 1.1-2 of the online notes
Course Goals
In this course we will extend our theory of calculus to cover functions of multiple variables. We will understand these functions algebraically and geometrically, and learn how to use the tools of differential and integral calculus to further understand them.
Topics will include: vectors, 3D graphing, planes, partial derivatives, directional derivatives, gradients, the chain rule, optimization and Lagrange multipliers, integration, vector fields, line and surface integrals, and Green’s, Stokes’s, and the Divergence theorem.
The course syllabus is available here.
Course notes
- Course Notes
- Section 1: Vectors in Space
- Section 2: Vector Functions
- Section 3: Partial Derivatives
- Section 4: Optimization
- Section 5: Multiple Integrals
- Section 6: Line Integrals
- Section 7: Surface Integrals
- Section 8: Divergence
Mastery Quizzes
Allocation of topics is tentative and may change as the course progresses.
- Mastery Quiz 1: Due September 7
- Mastery Quiz 2: Due September 12
- M1, S1
- No answer blanks
- Answer blanks
- Solutions
- Everyone should submit both questions on this quiz. I screwed up, and the “vectors” topic that we started last week is in fact a major topic. You get four cracks at it, and will be graded on your best two. Everything is being updated to reflect that.
- Mastery Quiz 3: due September 19
- M1, S1, S2
- No answer blanks
- Answer blanks
- Solutions
- Mastery Quiz 4: due September 26
- M1, M2, S2, S3: due
- No answer blanks
- Answer blanks
- Solutions
- Mastery Quiz 5: Due October 10
- No answer blanks
- Answer blanks
- M2, M3, S3
- Solutions
- Mastery Quiz 6: due October 17
- Mastery Quiz 7: due October 26
- Mastery Quiz 8: due October 31
- Mastery Quiz 9: due November 7
- Mastery Quiz 10: due November 21
- M4, M5, S4
- No answer blanks
- Answer blanks
- Solutions
- Mastery Quiz 11: due November 28
- M4, M5, S5
- No answer blanks
- Answer blanks
- Solutions
- Mastery Quiz 12: due December 5
- M5, M6, S5
- No answer blanks
- Answer blanks
- Solutions
- Mastery Quiz 13: due December 12
Major Topics
- Vectors
- Partial Derivatives
- Optimization
- Multiple Integrals
- Line Integrals
- Surface Integrals
Secondary Topics
- Lines and Planes
- Vector Functions
- Multivariable Functions
- Integral Applications
- Vector Fields
- The Divergence Theorem
Tests
- Midterm on October 3
- Midterm on November 14
- Final Exam on Monday, December 19, 12:40 - 2:40 PM
Graphing calculators will not be allowed on tests. Scientific, non-programmable calculators will be allowed. I will have some to share, but not enough for everyone.
Textbook
The official textbook for Math 2233 is OpenStax Calculus Volume 3 by Gilbert Strang and Edwin Herman. It is available for free online here. You can also buy copies from Amazon; a paperback is a little under $30.
I will be loosely following the textbook, but will often be giving my own take or focusing on topics the textbook doesn’t emphasize. All my course notes will be posted to the course web page.
We will be using a (free!) online homework system called WeBWorK this term. You can access it by going to Blackboard, then to “Course Links”, and clicking the WeBWorK link. This will automatically create an account for you and log you in. You may continue to log in through Blackboard, or if you wish you may create a password within WeBWorK to log in directly.